The US authorities have no direct access to UK criminal records (including the finger print database). They only know about specific individuals where the UK has passed relevant information on. It's likely that your boyfriend would be able to enter the USA (illegally) under the Visa Waiver Program. (One AB contributor has stated that he's got Class A drug convictions and has entered the USA several times with no problems).
As others have stated, it's unlikely that your boyfriend would get a visa if he applied for one but, as long he's prepared to accept a small element of risk, he'd probably get in under the Visa Waiver Program.
Chris